Abstract

The Bézier curve is a continuous parametric curve that is used in numerous applications, such as automobile design and road design. I begin by surveying the fundamental properties of the Bézier curve and provide a variety of examples and calculations. I also survey, but more succinctly, the notion of the Bézier surface, which also has numerous applications in computer-aided design software, such as aircraft design. I end by presenting the special types of points that a cubic Bézier curve (with four control points) can have. The configuration of planar control points that I present can be used by computer engineers to produce various shapes with respect to the necessary design requirements and to minimize fluctuations of the curve itself.